Question

F(x)=-x+5;g(x)=2f(x) i need to know the horizontal stretch and by. also f(x)=2x+3; g(x)=f(x)+3

Answer 1

For the first equation:

`f(x)=-x+5,g(x)=2f(x)`

That's a vertical stretch by 2. If you change f(x) for 'y' you'll see that more clearly:

`y=-x+5,g(x)=2y`

All 'y' coordinates of the function are now twice as before. This means that the function is stretched vertically.

For the second:

`f(x)=x-4,g(x)=-f(x)`

We'll change f(x) for 'y' too:

`y=x-4,g(x)=-y`

That is a reflection over the x axis. This is because in order to go from y to -y all 'y' coordinates of the points on the function have to change from possitive to negative and from negative to possitive. In a graph: